We use broadband photometry extending from the rest-frame UV to the near-IR to fit the individual spectral energy distributions of 63 bright (L(Ly-alpha) greater than 10(exp 43) erg s(exp -1) Ly-alpha emitting galaxies (LAEs) in the redshift range 1.9 less than z less than 3.6. We find that these LAEs are quite heterogeneous, with stellar masses that span over three orders of magnitude, from 7.5 greater than logM/solar mass less than 10.5. Moreover, although most LAEs have small amounts of extinction, some high-mass objects have stellar reddenings as large as E(B - V ) is approximately 0.4. Interestingly, in dusty objects the optical depths for Ly-alpha and the UV continuum are always similar, indicating that Lya photons are not undergoing many scatters before escaping their galaxy. In contrast, the ratio of optical depths in low-reddening systems can vary widely, illustrating the diverse nature of the systems. Finally, we show that in the star-formation-rate-log-mass diagram, our LAEs fall above the "main-sequence" defined by z is approximately 3 continuum selected star-forming galaxies. In this respect, they are similar to submillimeter-selected galaxies, although most LAEs have much lower mass.